Question

3 years from now will be 360. We would like I THU
(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been
8 km/h less, then it would have taken 3 hours more to cover the same distance. We
need to find the speed of the train. a quadratic equation for this??? ​

Answer 1

Answer

Let the speed of the train be x km/hr. Then

Time taken to travel a distance of 480km=

x

480

hr

Time taken by the train to travel a distance of 480km with the speed (x−8)km/hr=

x−8

480

hr

It is given that if the speed had been 8km/hr less, then the train would have taken 3 hours more to cover the same distance

∴

x−8

480

=

x

480

+3

⇒

x−8

480

−

x

480

=3⇒

x(x−8)

480(x−x+8)

=3⇒

x(x−8)

480×8

=3

⇒3x(x−8)=480×8⇒x(x−8)=160×8⇒x

2

−8x−1280=0

This is the required quadratic equation.

Answer 2

: ANSWER

The speed of train is = 40 km /hr

: GIVEN

Distance covered = 480 km

if the speed has been 8 km / hr less

: FIND

Speed of the train

: SOLUTION

$\looparrowright$Let the normal speed be x km \hr

$\looparrowright$ We know that

$\looparrowright$ Time = Distance/ speed

$\mapsto$ $\frac{480}{x - 8} - \frac{480}{x} = 3$$\mapsto$ Cross multiplying

$\frac{480x - 480(x - 8)}{x(x - 8)} = 3$$\mapsto$ 480x - 480x + 3840=3(x2- 8x)

$\mapsto$ $3x {}^{2} - 24x - 3840 = 0$

$\looparrowright$ Factories by splitting the middle term

$\mapsto$ $x {}^{2} - 40x + 32x - 1280 = 0$

$\mapsto$ $x(x - 40) + 32(x - 40) = 0$

$\mapsto$ $(x - 40)(x + 32) = 0$

$\mapsto$ $x = - 32 \: x = 40$

$\looparrowright$ Here speed can't be negative

$\implies$ So, the train speed is 40 km /hr

$\sf \boxed{speed \: of \: the \: train \: is = 40 \: km \ \:hr}$